Deformations of free boundary CMC hypersurfaces
Renato G. Bettiol, Paolo Piccione, Bianca Santoro
TL;DR
This paper investigates how free boundary constant mean curvature hypersurfaces deform when considering ambient symmetries, allowing simultaneous variation of mean curvature and ambient metric, with applications to specific geometric shapes.
Contribution
It introduces a framework for analyzing deformations of free boundary CMC hypersurfaces considering ambient symmetries and variable mean curvature and metric.
Findings
Deformation theory for free boundary CMC hypersurfaces with degenerate Jacobi operators.
Application to free boundary CMC disks and Delaunay annuli in space form balls.
Abstract
We study deformations of free boundary constant mean curvature (CMC) hypersurfaces whose Jacobi operator is degenerate due to symmetries of the ambient space. The value of the mean curvature and the ambient metric are allowed to vary simultaneously, provided that the infinitesimal ambient symmetries change smoothly. We discuss applications to free boundary CMC disks and Delaunay annuli in the unit ball of a space form.
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